Additional ways to pin:
I. The key to the pin is playing multiple dead masqs (ones where you have no cards in deck to pass)
Golem - you can play 2 dead masqs if you discard two masqs or return two masqs to the deck. With a KC you can burn up to 4 cards this way.
E.g.:
Oasis (discard masq) -> Oasis (discard KC) -> Golem (masq, KC -> masq)
You can get clever and bury things on the NV mat and use NV to get additional dead masqs in play with golem. Obviously this requires a lot of cards and needs something phenomenal in the way of deck reliability (e.g. haven x2/SP x2, scheme, etc.).
E.g.:
Village -> Embassy (discard masq, KC, cantrip) -> KC -> NV (place discard on mat) -> secret chamber (discard KC, NV) -> golem (KC -> masq, NV) -> cantrip -> KC -> masq
Outpost, for either a deck that has 4 cards (including outpost) or for an engine that is very reliable can allow you to double the plays of dead masqs (whatever that is).
E.g.:
village -> outpost -> KC -> masq
village -> KC -> masq
Both TR and KC can be used to play multiple dead masqs; however each is hard capped at 2 or 3 dead masqs respectively unless golem or NV is used to enable further dead plays.
When you combine everything, you can actually build a theoretically workable, unblockable (excepting durations) 4 player pin. You will never build that pin in anything approaching a real game [setup -> Golem (KC -> masq, NV) -> setup -> Golem (KC -> masq, NV) -> outpost -> KC -> masq; repeat during outpost turn]
II.
Another shot is to reduce the number of needed dead masqs by having your opponent discard. Every expansion except Alchemy has a mandatory discard. Of those, minion and followers are the only ones that don't work as a simple replacement for goons. KC/KC/Ghost Ship/Masq leaves the other guy just as dead as goons. Followers comes with an estate so you will burn one fewer card until the estate pile runs out - then you are good to go. Minion requires that you get 4 cards out of their hand, this is most easily done with outpost or golem. This is what I think is the most versatile pin:
Minion -> TR -> TR -> outpost -> masq
Minion -> TR -> masq
You can also try to hand deplete with conditional hits - cut purse and B-crat at this point. B-crat is virtually unworkable; KC/KC/B-crat/WT/Masq works to pin the opponent down to two (or three) green cards (nobles, islands, estates, whatever), you can use the WT to trash inbound silver, and the masq kills three (two) other cards. Cut purse works similarly except that it targets coppers (and they start with 7), cards are discarded (so they don't get to say keep 3 provinces when there are only 15 points left on the board), and there isn't a flood of treasure coming in. Additionally, you can add coppers to the opponent's deck with either mountebank or noble brigand; eventually this forces the pin to hit. E.g. KC/KC/CP/NB/Masq will try to discard 3 coppers from the opponent's hand. If it hits 2 or 3 coppers, then the opponent begins next hand with 0 cards and his deck has 2 fewer "not copper" cards. NB steals treasure (which can be problematic for the pin) and floods him with coppers if he doesn't have any. Long story, short, eventually you will pin the opponent, but the game has good odds of ending first.
III. Fighting the pin.
The pin is weak against its own components. Masq can steal irreplaceable cards, discard attacks make it harder (though not impossible) to string together the combo (e.g. KC/KC/goons/masq is DoA if you play a goons every turn). The pin player can overbuild the pin to have spare cards to send over (e.g. KC/KC/Militia/Militia/Masq can lose a militia & still pin) or have live draw to get back up to the needed 4 cards (e.g. KC/KC/Margrave can draw a masq to play; KC/KC/village can draw a militia and masq & proceed to pin). Using a discard attack and masq after that makes it very hard for a pin player to maintain their deck for the pin. KC/KC/village/militia/masq will most likely go down to KC/KC/village and either has to pass the village (you live for another day) or pass the KC (which means you lose one card this time and they buy a village; village/village/KC/miltia/masq will have the same problem if it gets hit with discard & masq).
Durations allow you to play after having lost all your other cards (and getting to play a masq off a tac or haven is huge). Moat, lighthouse, and horse traders lets you keep some cards and play against attack pins (those using golems or outpost are unaffected).
Another shot is getting a game ending megaturn out before the pin hits. KC/KC/Bridge/Bridge/Bridge does this (though you need to be sure to either slow down the pin with attacks or have strong enablers for the KC/Bridge combo). Other options that might be viable on particular boards include mass HoP, KC/Bridge(Highway)/IW/Nobles, etc.